The Greens may yet thwart Malcolm Turnbull's ambition of a major win when federal parliament sits for the final week before the long winter break.
The Greens say they won't be rushed into passing the schools funding plan which is scheduled for Senate debate on Wednesday, despite being offered a compromise package.
With Labor opposed to the so-called Gonski 2.0 funding model, the prime minister needs the support of the nine Greens and at at least one other crossbencher to achieve the extra 10 votes needed to pass the bill.
Education Minister Simon Birmingham has offered a compromise to the Greens that includes getting money to schools faster than the planned 10 years, more accountability over state government funding, and an independent watchdog.
Catholic schools, which believe they will be worse off than under present funding arrangements, say Senator Birmingham is desperately trying to get his policy passed this week.
"So it is important that Catholic school parents and the wider community understand the implications of this school funding model," National Catholic Education Commission executive director Christian Zahra says.
"They can then make sure their elected representatives hear their concerns and hear about the damaging consequences of locking in an ill-considered policy, especially when it's being locked in for 10 years."
Mr Turnbull is likely to have better luck with his major bank levy, which will be debated in the lower house on Monday before heading to the Senate, where Labor is expected to give it the tick.
A bill to set up the Medicare Guarantee Fund, which would set aside money for Medicare payments and the Pharmaceutical Benefits Scheme, is also before the parliament.
The nation's big media companies are hopeful a deal can be struck on broadcasting reforms.
But it's unclear where the government will get the numbers, given Labor remains opposed to axing the rule which bans companies from controlling more than two out of three print, radio and television outlets in the one market.
Private member's business in the lower house on Monday will focus on two bills to protect penalty rates.
On Tuesday, retiring Liberal senator Chris Back will deliver his valedictory address and newcomer Lucy Gichuhi will give her first speech on Wednesday.
The Senate's economics committee will hear on Monday from submarine maker DCNS and the Defence Department on the government's naval shipbuilding industry plans.
Also on Monday the joint treaties committee will probe amendments to the Singapore-Australia free trade agreement.
Senate inquiry reports are due on the major bank levy, Australian veterans, the Bell Group litigation and the insurance industry.